An exploration of alternative methods to deal with time-varying selectivity in the stock assessment of YFT in the eastern Pacific Ocean CAPAM – Selectivity Workshop La Jolla, USA, March, 2013 Alexandre Aires-da-Silva and Mark Maunder

Outline Background on YFT assessment  Stock Synthesis (SS3) model  Selectivity issues: time-varying process  Retrospective pattern in recent recruitments Explore SS3 approaches to deal with time- varying selectivity  Ignore time-varying selectivity (base case model)  Full time-varying selectivity (deviates)  Time-varying for terminal years only

YFT fishery definitions

Quarterly time-step model Fishery definitions: 16 fisheries Data weighting: the CV of the southern LL fishery was fixed (0.2), others estimated (NOA, DEL) Growth modeling: Richards curve, L 2 and variance of length-at-age are fixed Modeling of catchability and selectivity:  Catchability coefficients for 5 CPUE time series are estimated (NOA-N, NOA-S, DEL-N, DEL-I, LL-S)  Size-based selectivity curves for 11 of the 16 fisheries are estimated (fit to size composition data)  Logistic selectivity for LL-S and DEL-S, and dome-shape for other fisheries YFT Stock Synthesis model

YFT size selectivity

OBJ time-varying selectivity? F1-OBJ_S F2-OBJ_C F3-OBJ_I F4-OBJ_N

OBJ LF residual pattern F1-OBJ_SF2-OBJ_C F3-OBJ_I F4-OBJ_N

Retrospective pattern

Projections CATCHES SPAWNING BIOMASS Purse seine Longline

Numerical and convergence issues Unstable selectivites (OBJ)  Sensitive to initial parameter values and phases  Long run times (> 4 hours)  Issues inverting hessian matrix (steepness run)

Objectives of study Test approaches available in SS to deal time- varying selectivity  Improve selectivity process (time-varying)  Minimize retrospective pattern  Shortcoming: more parameters, longer run times Simplify model  Less data, collapse fisheries (OBJ) Some considerations  We assume that retrospective pattern is mainly driven by model misfit to recent OBJ LF data caused by misspecified selectivity  We recognize that other sources of bias and misspecifcation may exist

F1-OBJ_S F2-OBJ_C F3-OBJ_I F4-OBJ_N A single “lumped” OBJ fishery

Model 0: Constant selectivity Selectivity: Estimate “average” constant selectivity Data: Fit to OBJ length-frequency data for all historic period Base case model configuration

Model 0: Constant selectivity

Model 1 - Full time-varying selectivity Selectivity: Quarterly time-varying selectivity Estimate quarterly deviates on base selex parameters of double normal OBJ selectivity curve Data: Fit to OBJ LF data for all historic period SD of quarterly deviates need to be defined:  First run: freely estimate devs with high flexibility (SD=1)  Second run: Use SD of estimated devs from first run in penalized likelihood approach

Model 1 - Full time-varying selectivity

Constant selectivity model 0 Time-variant model (M1-P2fix) Model 1 - Full time-varying selectivity

Model 2 – “hybrid” approach Recent period is the most influential on management quantities (recent recruitments, Fs) Time-varying selectivity process in recent period only Estimate quarterly deviates on base selex parameters of double normal OBJ selectivity curve Fit to OBJ LF data for recent period only  3 terminal years (3-year average used for management quantities)  5 terminal periods (a longer period) As for early period, fix to “average” constant selectivity from terminal years (base parameters)

Tvar selex- 3 years Tvar selex - 5 years Model 2 – “hybrid” approach

Tvar selex- 3 years Tvar selex - 5 years

Model 2 – “hybrid” approach

Conclusions Allowing for OBJ time-varying selectivity helped to minimize retrospective pattern in recent YFT recruitment estimates Balance between the amount of selectivity process (# of params.) needed in the model and the OBJ LF data to include in model fit (whole series or few recent years only?) Allowing for time-varying selectivity (quarterly deviates) in terminal years of the assessment only while fitting to LF data for this period seems a reasonable compromise An “average” constant selectivity curve is applied to the early period while not fitting to the LF data for that period A simulation study is needed to more rigorously investigate selectivity issues and associated bias in the YFT assessment

QUESTIONS?

Total catches

Fix selectivity Assume “average” stationary OBJ selectivity “Drop” (not fit) all OBJ LF data Fix to base selectivity parameters estimated in full time-varying runs (models 1) Models

Fix selectivity M2-P2fixed M2-P2est Models

Fix selectivity M2-P2fixed M2-P2est Models

Recruitment – all models

SBR – all models

Model type 1

Model type 3